Differential phase-shift keying (DPSK) has become the format of choice for long-haul optical transmission systems, due to the 3-dB improvement in receiver sensitivity compared to on-off keying and enhanced tolerance to dispersion and nonlinear effects, particularly intrachannel four-wave mixing (FWM). DPSK systems with balanced detection can tolerate a large amount of amplitude noise compared to on-off keying since, in DPSK systems, errors occur only when pulse-to-pulse phase relationships deviate by more than π/2 from their original values, regardless of the amplitude at detection. Excluding timing jitter, the primary limitation of a DPSK transmission system is the accumulation of linear and nonlinear phase noise.
Linear phase noise results from imperfections in optical modulators and from amplified spontaneous emission in optical amplifiers. Nonlinear phase noise results from intra- and inter-channel nonlinearities such as self phase modulation and cross phase modulation that convert amplitude noise to phase noise, which is known as the Gordon-Mollenauer effect. As a result, amplitude noise from modulators, ASE, dispersion-induced pattern effects and nonlinearities such as inter-channel FWM all introduce nonlinear phase noise that limits system performance.
As described in H. Kim and A. H. Gnauck, “Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise”, IEEE Photon. Technol. Lett. 15, pp. 320-322 (2003), when the nonlinear contribution to phase noise becomes dominant the 3-dB improvement in receiver sensitivity for balanced DPSK detection can be lost, negating a major advantage of using DPSK over on-off keying.
Several techniques suggested for managing fiber nonlinearity are described in C. Pare, A. Villeneuve, P. A. Belanger and N. J. Doran, “Compensating for dispersion and the nonlinear Kerr effect without phase conjugation,” Opt. Lett. 21, pp. 459-461 (1996); and I. R. Gabitov and P. M. Lushnikov, “Nonlinearity management in a dispersion managed system,” Opt. Lett. 27, pp. 113-115 (2002).
Another technique is to reduce the accumulation of nonlinear phase noise, including mid-link spectral inversion as disclosed in S. L. Jansen, D. van den Borne, G. D. Khoe, H. de Waardt, C. C. Monsalve, S. Spalter and P. M. Krummrich, “Reduction of nonlinear phase noise by mid-link spectral inversion in a DPSK based transmission system,” in proc. OFC, OTh05, Anaheim Calif., 2005. However these management schemes do not remove phase noise once it accumulates.
Post transmission nonlinear phase shift compensation (NLPSC) can effectively mitigate self phase modulation induced nonlinear phase noise as disclosed in X. Liu, X. Wei, R. E. Slusher and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27, pp. 1616-1618 (2002), and C. Xu and X. Liu, “Post-nonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27, pps. 1619-1621, (2002), but does not correct for linear phase noise or the effects of inter-channel cross phase modulation.
To accomplish DPSK regeneration it is necessary to equalize the pulse relative amplitudes while simultaneously restoring the encoded differential phase shifts. So far, the topic of DPSK regeneration has been divided between schemes that address amplitude and phase regeneration independently, since several traditional amplitude regeneration techniques inherently degrade phase information.
Phase-preserving DPSK amplitude regeneration is described in C. Xu and X. Liu, “Post-nonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. 27, pp. 1619-1621, (2002), is based on cross phase modulation combined with optical filtering described in A. Striegler and B. Schmauss, “All-Optical DPSK Signal Regeneration Based on Cross-Phase Modulation,” IEEE Photon. Tech. Lett. 16, pp. 1083-1085 (2004), and using a modified nonlinear optical loop mirror (NOLM) as described in A. Striegler, M. Meisaner, K. Cvecek, K. Sponsel, G. Leuchs and B. Schmauss, “NOLM-Based RZ-DPSK Signal Regeneration,” IEEE Photon. Technol. Lett. 17, pp. 639-641 (2005). However, these techniques have not been demonstrated experimentally.
Numerical analysis has shown that FWM-based amplitude regenerators are favorable for DPSK systems, since phase information can be preserved. See M. Matsumoto, “Regeneration of RZ-DPSK Signals by Fiber-Based All-Optical Regenerators,” IEEE Photon. Technol. Lett. 17, pp. 1055-1057 (2005). Phase-regenerative amplification of a DPSK signal suffering only phase noise has been demonstrated in a combined Sagnac-SOA structure for an input Q-factor>14 dB as described in P. S. Devgan, M. Shin, V. S. Grigoryan, J. Lasri and P. Kumar, “SOA-based regenerative amplification of phase noise degraded DPSK signals,” in proc. OFC, PDP34, Anaheim Calif., (2005).
The phase-sensitive amplifier (PSA) has emerged as an interesting candidate for optical amplification of both on-off keyed and DPSK signals. PSA's have been widely realized in nonlinear optical loop mirrors (NOLM) for amplification of high speed signals as disclosed in M. E. Marhic, C. H. Hsia and J. M. Jeong, “Optical Amplification in a nonlinear fiber interferometer,” Electron. Lett. 27, pp. 210-211 (1991).
Phase-sensitive amplifiers offer the potential of providing signal gain with a noise figure less than the 3-dB quantum limit of phase-insensitive amplifiers as described in W. Imajuku, A. Takada and Y. Yamabayashi, “Inline coherent optical amplifier with noise figure lower than 3 dB quantum limit,” Electron. Lett. 36, pp. 63-64 (2000).
PSA's also may act as limiting amplifiers as described in A. Takada and W. Imajuku, “Amplitude noise suppression using a high gain phase sensitive amplifier as a limiting amplifier,” Electron. Lett. 32, pp. 677-679 (1996).
PSA's also show regenerative characteristics when they are used to store solitons in optical buffers as described in G. D. Bartolini, D. K. Serkland, P. Kumar and W. L. Kath, “All-Optical Storage of a Picosecond-Pulse Packet Using Parametric Amplification,” IEEE Photon. Technol. Lett. 9, pp. 1020-1022 (1997).
Recently we proposed using a PSA for simultaneously regenerating both the amplitude and phase of a DPSK signal as disclosed in K. Croussore, C. Kim and G. Li, “All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification,” Opt. Lett. 28, 2357-2359 (2004), with the potential for restoring differential phase shifts to almost exactly 0 or π even for large values of input phase noise while restoring pulse amplitudes for >3-dB input amplitude noise. Two regimes of operation for the PSA-based DPSK regenerator were discussed: an un-depleted pump PSA, which performs nearly ideal phase-only regeneration, and a depleted-pump PSA that would combine phase and amplitude regeneration.